Authors:
A. Chuprunov Department of Math. Stat. and Probability, Chebotarev Inst. of Math. and Mechanics Kazan State University, Universitetskaya 17, 420008 Kazan, Russia

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I. Fazekas Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary

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Abstract  

An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme.

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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